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Description of a number slide |
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Example 1: The effect on 3.1 when it is multiplied and divided by powers of 10 |
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Example 2: The effect on 0.4 when it is multiplied and divided by powers of 10 |
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Example 3: The effect on 60 when it is multiplied and divided by powers of 10 |
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Teaching rules for working with powers of 10 |
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Making number slides (photocopy masters) |
Description of a number slide
A number slide is simple to make and ideal for learning to multiply and divide by ten and its powers (glossary). It is especially useful for illustrating that multiplication and division by powers of 10 do not move the decimal point. Rather the digits in the columns move to the left or right; the examples below demonstrate this feature in three cases. Emphasise the reasons for this rather than expect the students to memorise a rule such as "move the decimal point 2 places to the right" which is soon forgotten, or misapplied. As you read through these examples, you will see that in some cases zeros are introduced and in others they are omitted. The issue of When Do Zeros Matter? is a complex one which needs time to be thoroughly considered by students before they will be comfortable and competent with our place value notation.
Example 1:
In this example, a number slide is used to multiply 3.1 by 10 and by 100, and then 3.1 is divided by 10 and by 100. The arrows indicate the direction that the slide is moved.
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NUMBER SLIDE |
USUAL REPRESENTATION |
COMMENT |
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Original number.
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After multiplying by 10. Note the decimal point can be omitted as there is no decimal component. |
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After multiplying by another 10. Note the need for introducing a zero in the ones column. |
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Back to the original number.
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After dividing by 10. Note the additional zero in the ones column. |
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After dividing by another 10. Note the additional zero in the ones column as well as the tenths column. |
Example 2:
Here the results of multiplication and division by powers of 10 on 0.4 is illustrated.
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NUMBER SLIDE |
USUAL REPRESENTATION |
COMMENT |
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| 0.4 |
Original number.
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| 4 |
After multiplying by 10. Note the decimal point can be omitted as there is no decimal component. Further, the zero on the left is unnecessary. |
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| 40 |
After multiplying by another 10. Note the need for introducing a zero in the ones column, as well as omitting the zero on the left. |
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| 0.4 |
Back to the original number.
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| 0.04 |
After dividing by 10. Note the additional zero in the ones column.
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| 0.004 |
After dividing by another 10. Note the additional zero in the ones column as well as the tenths column.
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Example 3:
In this last example, the above procedures are applied to 60.
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NUMBER SLIDE |
USUAL REPRESENTATION |
COMMENT |
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Original number. |
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After multiplying by 10. Note the need for introducing a zero in the ones column. There is no need to introduce a decimal point as there is no decimal component. |
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After multiplying by another 10. Note the need for introducing a zero in the ones column, as well as in the tens column. |
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Back to the original number. |
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After dividing by 10. Note the removal of the zero in the tenths column and that the decimal point is not required. |
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After dividing by another 10. Note the additional zero in the ones column as well as the introduction of the decimal point. |
Teaching rules for working with powers of ten
Work with a number slide (with adequate discussion about why it works) can provide a firm foundation for the quick "appending zeros for multiplying by ten, hundred etc" rules that are important for everyday calculation. However, students must reach an understanding of a concept before learning a rule. Many students who are given a rule just give up trying to understand and so quickly forget. Nonetheless, it is essential that students learn to multiply by ten and its powers efficiently. Common errors such as 3.1 x 10 = 3.10 arise when students learn over-simplified rules parrot fashion. The best way is probably to encourage the students to make their own rules.
After students have used a number slide with various examples, they should be drawn to consider:
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the need for a number in the ones column (the basic building block and reference point for our number system) |
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the need to fill in any gaps between the original digits and the ones column with zeros |
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the need to remove unnecessary zeros or the decimal point. |
Making Number Slides
You may wish to make your own (print a photocopy master) or to buy commercially made number slides from an Australian supplier. (Here is another order form for further decimal and fraction activity materials).